* U.S. ISM softer than expected, weighs on dollar * Yen gains broadly but downtrend intact * Korean tensions buoy safe-haven yen * Thin trade allows yen to firm despite BoJ easing expectations By Julie Haviv NEW YORK, April 1 (Reuters) - The dollar slid to a nearly four-week low against the yen as softer-than-expected U.S. manufacturing data for March implied the economy may have run out of steam at the end of the first quarter, interrupting a recent run of generally upbeat reports. The euro, meanwhile, fell to an over one-month trough versus the yen as investors favored the safe-haven Japanese currency following unexpectedly weak Chinese factory activity and renewed uncertainty in the Korean peninsula. Volume, however, was thin, with many markets still closed for Easter holidays, and the low liquidity led to exaggerated currency moves. U.S. factory activity grew at the slowest rate in three months in March. The Institute for Supply Management said its index of national factory activity fell to 51.3 last month from 54.2 in February. A reading above 50 indicates expansion in the manufacturing sector. China's official Purchasing Managers Index reached 50.9 in March, just shy of market expectations of a jump to 52 from February's 50.1. "The dollar sold off versus the yen after the disappointing ISM data, but trade is very thin and investors are likely using the data as an excuse to lighten dollar positions ahead of this week's events," said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington D.C. The European Central Bank and Bank of Japan both hold monetary policy meetings this week. With the path of Federal Reserve policy largely hinging on the state of the U.S. labor market, Friday's U.S. payrolls data has the potential to sway financial markets. "There is a lot of optimism already priced into the dollar regarding the U.S. economy and the dollar could be poised for a sell-off should upcoming data disappoint," Esiner said. The greenback has been in a broad rally this year as evidence mounted that the U.S. economy is on a stable path to recovery. The dollar index has gained about 3.6 percent so far in 2013."There are some clear signs that recent growth momentum in the manufacturing sector will not be easily built," said Alan Ruskin, head of G10 FX strategy at Deutsche Bank in New York. "The data will tend to undercut some of the enthusiasm in the long dollar exposure." Ruskin pointed out that it's not all "gloom and doom" for the U.S. manufacturing report, with both the employment and new orders components posting new highs. The dollar fell nearly 1.0 percent to 93.28 yen, falling as low as 93.16, the lowest since March 6. The euro slid 0.7 percent to 119.92 yen, the lowest since Feb. 27. KOREAN TENSIONS Tensions in the Korean Peninsula also supported the yen, analysts said. South Korea on Monday said it will strike back quickly if the North stages any attack on its territory after North Korea earlier said the region is on the brink of a nuclear war. Investors had earlier brushed off a disappointingly narrow improvement in Japanese business sentiment over the last quarter shown by the Bank of Japan's tankan survey, as the focus is more on the central bank's policy review later in the week. The BoJ is widely expected to scale up its bond buying and to extend the maturities of the bonds it purchases under new Governor Haruhiko Kuroda. Bets on a radical shift in the BoJ's policy has ramped the dollar up 20.9 percent against the yen in the last two quarters, pushing it to a 3-1/2-year high of 96.71 yen last month. The euro, meanwhile, was up 0.3 percent against the dollar at $1.2852, rallying from a low of $1.2770. Europe's common currency was still down 2.6 percent so far this year and has slid steadily since February, when it hit a 14-month high of $1.3711. Meanwhile, over the weekend, the Cypriot central bank confirmed that major depositors in Cyprus's biggest bank would lose around 60 percent of savings over 100,000 euros, well above the initially touted cut of 30 to 40 percent. The euro has major support around $1.2680, a 61.8 percent retracement of its July-February rally. But a break there could open the way for a test of last year's low near $1.20. Borrowing costs in Slovenia, seen by economists as one of the next potential candidates for the next euro zone bailout, jumped in the wake of the Cyprus bailout, while Italian borrowing costs reached their highest since November at a five-year bond auction last week. Appetite for Italian debt has been hurt by the deadlock in the country's politics since inconclusive elections a month ago, reinforcing the euro zone common currency's weakness.